Involution

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involution

[‚in·və′lü·shən]
(biology)
A turning or rolling in.
(embryology)
Gastrulation by ingrowth of blastomeres around the dorsal lip.
(mathematics)
Any transformation that is its own inverse.
In particular, a correspondence between the points on a line that is its own inverse, given algebraically by x ′ = (ax + b)/(cx-a), where a 2+ bc ≠ 0.
A correspondence between the lines passing through a given point on a plane such that corresponding lines pass through corresponding points of an involution of points on a line.
(medicine)
The retrogressive change to their normal condition that organs undergo after fulfilling their functional purposes, as the uterus after pregnancy.
The period of regression or the processes of decline or decay which occur in the human constitution after middle life.

Involution

 

(raising to a power), an algebraic operation consisting in repeating a quantity a n number of times:

The number a is the base of the power, n is the exponent, and an is the power. For example, 3x3x3x3 = 34 = 81. The second power of a number is called its square and the third power, its cube.


Involution

 

(regression), in biology, a reduction or loss, in the process of evolution, of certain organs, and a simplification of their organization and functions (for example, various degrees of intestinal reduction in certain parasitic worms and arthropods). Degenerative changes in protozoans and bacteria caused by unfavorable conditions in the habitat are also called involutional. In medicine, the term sometimes refers to atrophy of organs and tissues, such as in aging.

References in periodicals archive ?
Here we find results of Newlander-Nirenberg [NN] for involutive almost complex structures and Kuranishi [K] and Akahori [Al for strictly pseudoconvex CR structures.
omicron]]) is then said to form an involutive quantaloid; we shall often simply speak of "an involutive quantaloid Q", leaving the notation for the involution understood.
The sequence (0) is the only involutive sequence of length 1.
Involutive transformations play an important role in integrable dynamical systems, see e.
The induced maps [lambda] [right arrow] [lambda]', T([lambda]) [right arrow] T([lambda]') and H([lambda]) [right arrow] H([lambda]') are obviously bijective and involutive in the sense that (x')' = x, (T')' = T, and (H')' = H.
For instance, the problem to find which automorphisms are involutive reduces to determine which g satisfy
As we will see, in an almost Kenmotsu manifold h = 0 means that the canonical foliation F, generated by the involutive 1-dimensional distribution ker([phi]) and called Reeb foliation, is conformal.
If P is a finite poset, it is shown in Cameron and Fon-Der-Flaass (1995) that the Fon-Der-Flaass action [PSI] may be expressed as a product of the involutive generators [{[t.
There is a natural involutive automorphism [phi] [right arrow] [bar.
1] the foliation on M defined by the involutive distribution [D.
1] is an involutive anti-automorphism of BFQSym, hence of MR.